Next, we take the large-\(R\)  limit, with the ratio \(R/t_{0}\)  kept fixed. We want to keep this latter ratio fixed so that the strip remains on the same boosted timeslice as we make the half-width larger and larger. We expect that \(z_{m} \approx z_{h} = 1\)  in the large-\(R\)  limit (indeed it is well-known that the horizon acts as a barrier to extremal surfaces [1]}, [2]}). So, for the rest of this section, \(z_{m}\)  will be taken to be close to the horizon. We also need to find the approximate value of \(p_{x}\) . This can be done by noting that the integral (REF ) for \(R\)  receives the largest contribution from the values of \(z^{\prime }\)  for which \(H(z^{\prime })\)  is small.
